Question: Simplify the following expression: $a = \dfrac{z^2 + 7z + 6}{z + 1} $
Explanation: First factor the polynomial in the numerator. $ z^2 + 7z + 6 = (z + 1)(z + 6) $ So we can rewrite the expression as: $a = \dfrac{(z + 1)(z + 6)}{z + 1} $ We can divide the numerator and denominator by $(z + 1)$ on condition that $z \neq -1$ Therefore $a = z + 6; z \neq -1$